Can a dual citizen petition his wife if he has no work and is living outside the US?

Yes, a U.S. citizen (even a dual citizen) who becomes married to a foreign national spouse may succeed with consular processing for the spouse so she may enter the U.S. and become a Permanent Resident. This is true even if the U.S. citizen is unemployed, although in that instance it may be necessary to have a "joint sponsor." Generally, any U.S. citizen or Permanent Resident who has sufficient documentable income and who is willing to assume the responsibilities contemplated in the Affidavit of Support may serve as a joint sponsor. It would be wise for your brother and his wife to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain the couple's goals, and who then could offer legal representation in the often complex application process.